The agency quoted Kayvan Khosravi, spokesman for Iran’s top security body, as saying on Sunday that Iran was also closing its airspace to flights originating in Iraqi Kurdistan.
The announcement came as Iran also started military exercises at the Kurdish border.
The air embargo is the first concrete retaliatory measure against Monday’s referendum which is rejected by the government in Baghdad and by Iraq’s powerful neighbours – Iran and Turkey – as well as western powers, including the US.
Reporting from Erbil, the regional capital of Iraqi Kurdistan, Al Jazeera’s Hoda Abdel Hamid said that Iran’s decision was expected by the Kurdish people.
“They are more disappointed with the international community’s reaction opposing the vote,” Abdel Hamid said.
The shutdown will affect two airports in the Kurdish area: in Erbil and Sulaymaniyah.
Abdel Hamid said that despite the air blockade, the land border between Iran and Iraq’s Kurdish region remains open.
The Kurdish region is one of Iran’s largest trading partner with about $4bn in trade every year.
On Saturday, the Turkish parliament approved the extension of a mandate allowing the deployment of troops in Iraq and Syria.